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Theory of Probability and Mathematical Statistics

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Strong stability in a $ G/M/1$ queueing system


Authors: Mustapha Benaouicha and Djamil Aissani
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 71 (2004).
Journal: Theor. Probability and Math. Statist. 71 (2005), 25-36
MSC (2000): Primary 60K25, 68M20, 90B22
DOI: https://doi.org/10.1090/S0094-9000-05-00645-9
Published electronically: December 28, 2005
MathSciNet review: 2144318
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Abstract: In this paper, we study the strong stability of the stationary distribution of the imbedded Markov chain in the $ G/M/1$ queueing system, after perturbation of the service law (see Aissani, 1990, and Kartashov, 1981). We show that under some hypotheses, the characteristics of the $ G/G/1$ queueing system can be approximated by the corresponding characteristics of the $ G/M/1$ system. After clarifying the approximation conditions, we obtain the stability inequalities by exactly computing the constants.


References [Enhancements On Off] (What's this?)

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Additional Information

Mustapha Benaouicha
Affiliation: Laboratory of Modelization and Optimization of Systems, Faculty of Sciences and Engineer Sciences, University of Béjaia, 06000, Algeria

Djamil Aissani
Affiliation: Laboratory of Modelization and Optimization of Systems, Faculty of Sciences and Engineer Sciences, University of Béjaia, 06000, Algeria
Email: lamos_bejaia@hotmail.com

DOI: https://doi.org/10.1090/S0094-9000-05-00645-9
Keywords: Queueing systems, strong stability, uniform ergodicity, perturbations, stability inequalities
Received by editor(s): July 30, 2003
Published electronically: December 28, 2005
Article copyright: © Copyright 2005 American Mathematical Society